Finite Group Databasebeta

← C127×#13329 #44577002

Subgroups — C127×#13329 #44577002

Order 32512.

578 conjugacy classes of subgroups.

The subgroup lattice has 384 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q32×C127C211yesmaximal, characteristic, complemented
2C22×SD32×C127C211yesmaximal, characteristic
3C2×#495×C127C211yesmaximal, characteristic
4C2×#358×C127C211yesmaximal, characteristic, complemented
5C2×#357×C127C211yesmaximal, characteristic
6C127×#1969C211yesmaximal, characteristic, complemented
7C127×#1374C211yesmaximal, characteristic, complemented
8C22×Q16×C127C2211yescharacteristic
9C22×Q16×C127C2211yescharacteristic
10C22×SD16×C127—21no—
11C22×D8×C127C2211yescharacteristic
12C2×#124×C127—21no—
13C2×Q32×C127—22no—
14C2×Q32×C127—22no—
15C2×Q32×C127—22no—
16C2×SD32×C127—22no—
17C2×SD32×C127—22no—
18C2×SD32×C127—22no—
19C22×C16×C127C2211yescharacteristic
20C22×C16×C127C2211yescharacteristic
21#495×C127—22no—
22#495×C127—22no—
23C2×#107×C127C2211yescharacteristic
24C2×#103×C127—21no—
25C2×C4×C8×C127C2211yescharacteristic
26#391×C127—21no—
27#358×C127—22no—
28#357×C127—22no—
29C22×Q8×C127—21no—
30C22×Q8×C127—21no—
31C22×D4×C127—21no—
32C2×Q16×C127—21no—
33C2×Q16×C127—21no—
34C2×Q16×C127—21no—
35C2×Q16×C127—21no—
36C2×Q16×C127—21no—
37C2×Q16×C127—21no—
38C2×Q16×C127—21no—
39C2×Q16×C127—21no—
40C2×Q16×C127—21no—
41C2×Q16×C127—21no—
42C2×Q16×C127D412yes—
43C2×Q16×C127D412yes—
44C2×SD16×C127—24no—
45C2×SD16×C127—42no—
46C2×SD16×C127—42no—
47C2×D8×C127—21no—
48C2×D8×C127—21no—
49C2×D8×C127—21no—
50C2×D8×C127—21no—
51C2×D8×C127—21no—
52C2×D8×C127D412yes—
53C22×C8×C127D411yescharacteristic
54C22×C8×C127C2311yescharacteristic
55#124×C127—24no—
56#124×C127—42no—
57C2×C4⋊C4×C127—21no—
58C2×C22⋊C4×C127—42no—
59C2×C42×C127D411yescharacteristic
60Q32×C127—28no—
61SD32×C127—28no—
62C2×C16×C127—21no—
63C2×C16×C127—21no—
64C2×C16×C127—21no—
65C2×C16×C127—21no—
66C2×C16×C127D412yes—
67C2×C16×C127D412yes—
68#107×C127—21no—
69#107×C127—21no—
70#103×C127—42no—
71C4×C8×C127—21no—
72C4×C8×C127—21no—
73#95×C127—42no—
74C24×C127—41no—
75C2×Q8×C127—22no—
76C2×Q8×C127—22no—
77C2×Q8×C127—41no—
78C2×Q8×C127—41no—
79C2×Q8×C127—41no—
80C2×Q8×C127—41no—
81C2×Q8×C127—41no—
82C2×Q8×C127—41no—
83C2×Q8×C127—41no—
84C2×Q8×C127—41no—
85C2×Q8×C127—41no—
86C2×Q8×C127—41no—
87C2×D4×C127—22no—
88C2×D4×C127—41no—
89C2×D4×C127—41no—
90C2×D4×C127—41no—
91C2×D4×C127—41no—
92C2×D4×C127—41no—
93C22×C4×C127—41no—
94C22×C4×C127—41no—
95C22×C4×C127—41no—
96C22×C4×C127D812yes—
97C22×C4×C127C2×D411yescharacteristic
98Q16×C127—22no—
99Q16×C127—22no—
100Q16×C127—22no—
101Q16×C127—22no—
102Q16×C127—41no—
103Q16×C127—41no—
104Q16×C127—41no—
105Q16×C127—41no—
106SD16×C127—48no—
107D8×C127—22no—
108D8×C127—22no—
109D8×C127—41no—
110D8×C127—41no—
111C2×C8×C127—21no—
112C2×C8×C127—21no—
113C2×C8×C127D812yes—
114C2×C8×C127C2×D411yescharacteristic
115C2×C8×C127C2×D411yescharacteristic
116C2×C8×C127C2×D411yescharacteristic
117C2×C8×C127C2×D411yescharacteristic
118C2×C8×C127C2×D411yescharacteristic
119C2×C8×C127#4111yescharacteristic
120C4⋊C4×C127—41no—
121C4⋊C4×C127—41no—
122C22⋊C4×C127—48no—
123C42×C127—21no—
124C42×C127—21no—
125C16×C127—22no—
126C16×C127—22no—
127C23×C127—42no—
128C23×C127—81no—
129C23×C127—81no—
130C23×C127—82no—
131C23×C127—82no—
132C23×C127C2×D811yescharacteristic
133Q8×C127—42no—
134Q8×C127—42no—
135Q8×C127—42no—
136Q8×C127—42no—
137Q8×C127—81no—
138Q8×C127—81no—
139Q8×C127—81no—
140Q8×C127—81no—
141D4×C127—42no—
142D4×C127—42no—
143D4×C127—81no—
144D4×C127—81no—
145C2×C4×C127—22no—
146C2×C4×C127—22no—
147C2×C4×C127—22no—
148C2×C4×C127—42no—
149C2×C4×C127—42no—
150C2×C4×C127—81no—
151C2×C4×C127—81no—
152C2×C4×C127—81no—
153C2×C4×C127—81no—
154C2×C4×C127—81no—
155C2×C4×C127—82no—
156C2×C4×C127#12011yescharacteristic
157C2×C4×C127#12111yescharacteristic
158C2×C4×C127#12711yescharacteristic
159C2×C4×C127C2×D811yescharacteristic
160C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
161C2×C4×C127AGL(1,ℤ/8)11yescharacteristic
162C8×C127—22no—
163C8×C127#12011yescharacteristic
164C8×C127#12011yescharacteristic
165C8×C127#12111yescharacteristic
166C8×C127#12111yescharacteristic
167C22×C127—84no—
168C22×C127—82no—
169C22×C127—162no—
170C22×C127—161no—
171C22×C127—161no—
172C22×C127#44711yescharacteristic
173C22×C127#45911yescharacteristic
174C22×C127#49311yescharacteristic
175C22×C127#50812yes—
176C22×C127#51012yes—
177C4×C127—42no—
178C4×C127—82no—
179C4×C127—82no—
180C4×C127—161no—
181C4×C127#39211yescharacteristic
182C4×C127#44711yescharacteristic
183C4×C127#45911yescharacteristic
184C4×C127#49611yescharacteristic
185#13329C12711yesmaximal, characteristic, direct product factor, Sylow
186C2×C127—162no—
187C2×C127#201111yescharacteristic
188C2×C127#218912yes—
189C2×C127#221112yes—
190C2×C127#224911yescharacteristic
191C2×C127#225111yescharacteristic
192C22×Q32C2×C12711yescharacteristic, complemented
193C22×SD32C2×C12711yescharacteristic
194C2×#495C2×C12711yescharacteristic
195C2×#358C2×C12711yescharacteristic, complemented
196C2×#357C2×C12711yescharacteristic
197#1969C2×C12711yescharacteristic, complemented
198#1374C2×C12711yescharacteristic, complemented
199C127#1332911yescharacteristic, direct product factor, Sylow
200C22×Q16C22×C12711yescharacteristic
201C22×Q16C22×C12711yescharacteristic
202C22×SD16—21no—
203C22×D8C22×C12711yescharacteristic
204C2×#124—21no—
205C2×Q32—22no—
206C2×Q32—22no—
207C2×Q32—22no—
208C2×SD32—22no—
209C2×SD32—22no—
210C2×SD32—22no—
211C22×C16C22×C12711yescharacteristic
212C22×C16C22×C12711yescharacteristic
213#495—22no—
214#495—22no—
215C2×#107C22×C12711yescharacteristic
216C2×#103—21no—
217C2×C4×C8C22×C12711yescharacteristic
218#391—21no—
219#358—22no—
220#357—22no—
221C22×Q8—21no—
222C22×Q8—21no—
223C22×D4—21no—
224C2×Q16—21no—
225C2×Q16—21no—
226C2×Q16—21no—
227C2×Q16—21no—
228C2×Q16—21no—
229C2×Q16—21no—
230C2×Q16—21no—
231C2×Q16—21no—
232C2×Q16—21no—
233C2×Q16—21no—
234C2×Q16D4×C12712yes—
235C2×Q16D4×C12712yes—
236C2×SD16—24no—
237C2×SD16—42no—
238C2×SD16—42no—
239C2×D8—21no—
240C2×D8—21no—
241C2×D8—21no—
242C2×D8—21no—
243C2×D8—21no—
244C2×D8D4×C12712yes—
245C22×C8D4×C12711yescharacteristic
246C22×C8C23×C12711yescharacteristic
247#124—24no—
248#124—42no—
249C2×C4⋊C4—21no—
250C2×C22⋊C4—42no—
251C2×C42D4×C12711yescharacteristic
252Q32—28no—
253SD32—28no—
254C2×C16—21no—
255C2×C16—21no—
256C2×C16—21no—
257C2×C16—21no—
258C2×C16D4×C12712yes—
259C2×C16D4×C12712yes—
260#107—21no—
261#107—21no—
262#103—42no—
263C4×C8—21no—
264C4×C8—21no—
265#95—42no—
266C24—41no—
267C2×Q8—22no—
268C2×Q8—22no—
269C2×Q8—41no—
270C2×Q8—41no—
271C2×Q8—41no—
272C2×Q8—41no—
273C2×Q8—41no—
274C2×Q8—41no—
275C2×Q8—41no—
276C2×Q8—41no—
277C2×Q8—41no—
278C2×Q8—41no—
279C2×D4—22no—
280C2×D4—41no—
281C2×D4—41no—
282C2×D4—41no—
283C2×D4—41no—
284C2×D4—41no—
285C22×C4—41no—
286C22×C4—41no—
287C22×C4—41no—
288C22×C4D8×C12712yes—
289C22×C4C2×D4×C12711yescharacteristic
290Q16—22no—
291Q16—22no—
292Q16—22no—
293Q16—22no—
294Q16—41no—
295Q16—41no—
296Q16—41no—
297Q16—41no—
298SD16—48no—
299D8—22no—
300D8—22no—
301D8—41no—
302D8—41no—
303C2×C8—21no—
304C2×C8—21no—
305C2×C8D8×C12712yes—
306C2×C8C2×D4×C12711yescharacteristic
307C2×C8C2×D4×C12711yescharacteristic
308C2×C8C2×D4×C12711yescharacteristic
309C2×C8C2×D4×C12711yescharacteristic
310C2×C8C2×D4×C12711yescharacteristic
311C2×C8#41×C12711yescharacteristic
312C4⋊C4—41no—
313C4⋊C4—41no—
314C22⋊C4—48no—
315C42—21no—
316C42—21no—
317C16—22no—
318C16—22no—
319C23—42no—
320C23—82no—
321C23—82no—
322C23—81no—
323C23—81no—
324C23C2×D8×C12711yescharacteristic
325Q8—42no—
326Q8—42no—
327Q8—42no—
328Q8—42no—
329Q8—81no—
330Q8—81no—
331Q8—81no—
332Q8—81no—
333D4—42no—
334D4—42no—
335D4—81no—
336D4—81no—
337C2×C4—22no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—42no—
341C2×C4—42no—
342C2×C4—81no—
343C2×C4—81no—
344C2×C4—81no—
345C2×C4—81no—
346C2×C4—82no—
347C2×C4—81no—
348C2×C4#120×C12711yescharacteristic
349C2×C4#121×C12711yescharacteristic
350C2×C4#127×C12711yescharacteristic
351C2×C4C2×D8×C12711yescharacteristic
352C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
353C2×C4AGL(1,ℤ/8)×C12711yescharacteristic
354C8—22no—
355C8#120×C12711yescharacteristic
356C8#120×C12711yescharacteristic
357C8#121×C12711yescharacteristic
358C8#121×C12711yescharacteristic
359C22—84no—
360C22—82no—
361C22—162no—
362C22—161no—
363C22—161no—
364C22#447×C12711yescharacteristic
365C22#459×C12711yescharacteristic
366C22#493×C12711yescharacteristic
367C22#508×C12712yes—
368C22#510×C12712yes—
369C4—42no—
370C4—82no—
371C4—82no—
372C4—161no—
373C4#392×C12711yescharacteristic
374C4#447×C12711yescharacteristic
375C4#459×C12711yescharacteristic
376C4#496×C12711yescharacteristic
377C2—162no—
378C2C127×#201111yescharacteristic
379C2C127×#218912yes—
380C2C127×#221112yes—
381C2C127×#224911yescharacteristic
382C2C127×#225111yescharacteristic
subgroupG/H
center, socleC23×C127C2×D8
commutator, Frattini, cosocleC22×C8C23×C127
prime radicalC22×D8×C127C22
LCSG ▷ C22×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C127 ◁ C2×C42×C127 ◁ C2×C4×C8×C127 ◁ G

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C22×Q32×C127C2semidirect
4. C2×#358×C127C2semidirect
6. C127×#1969C2semidirect
7. C127×#1374C2semidirect
185. #13329C127direct (N × H)
192. C22×Q32C2×C127semidirect
195. C2×#358C2×C127semidirect
197. #1969C2×C127semidirect
198. #1374C2×C127semidirect
199. C127#13329direct (N × H)

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C22×Q32×C1272
C22×SD32×C1272
C2×#495×C1272
C2×#358×C1272
C2×#357×C1272
C127×#19692
C127×#13742
#13329127